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Frequency-Domain Fast Maximum Likelihood Estimation of Complex Modes
Published in Jian Zhang, Zhishen Wu, Mohammad Noori, Yong Li, Experimental Vibration Analysis for Civil Structures, 2020
Recently, a fast algorithm (Au, 2012) for Bayesian fast Fourier transform (FFT) method has been developed for OMA. It can identify well-separated modes at the speed of seconds and closely spaced modes in less than 1 min with the identification error quantified, making it an ideal tool for practical applications. However, this method assumes a proportional damping, which may not capture the true dynamic characteristics of structures, e.g., when damper is introduced to suppress the vibration. This paper aims at developing its counterpart for the general non-proportional damping but with the principle of maximum likelihood (ML). In fact, the ML estimator should coincide with the Bayes estimator when the data is long enough, and especially the non-informative prior is used in the Bayesian inference. The potential gain of an ML estimator is that the identification uncertainty can be more efficiently computed. Unlike the fast algorithm (Au, 2012), which requires profound mathematical skill to understand and adept coding ability to program, we rely on the expectation-maximization (EM) algorithm to develop the ML estimation, yielding an easy-to-understand and simple-to-program approach.
Estimation and Prediction for the Power-Exponential Hazard Rate Distribution Based on Record Data
Published in American Journal of Mathematical and Management Sciences, 2020
Bahman Tarvirdizade, Nader Nematollahi
One of the attractive methods of estimation of the parameters of a distribution is the Bayes estimation. In this method, for estimation the parameter θ by the estimator the researcher needs a prior distribution, for θ, as well as a loss function, for estimation process. The Bayes estimate of θ is obtained by minimizing the posterior risk with respect to θ.
E-Bayesian inference for xgamma distribution under progressive type II censoring with binomial removals and their applications
Published in International Journal of Modelling and Simulation, 2023
Anurag Pathak, Manoj Kumar, Sanjay Kumar Singh, Umesh Singh, Manoj Kumar Tiwari, Sandeep Kumar
In this section, we have obtained the Bayes estimators of the parameter based on PT II CBRs. In order to obtain the Bayes estimator, we must assume that the parameter is random variable. We further assume that random variable has informative prior distribution with prior PDF,